Abstract
Motivated by the theories of Hecke algebras and Schur algebras, we consider in this paper the algebra CMGofG-invariants of a finite monoidMwith unit groupG. IfMis a regular “balanced” monoid, we show that CMGis a quasi-hereditary algebra. In such a case, we find the blocks of CMGto be the “sections” of the blocks of CM. We go on to develop a theory of cuspidal representations for balanced monoids. We then apply our results to the full transformation semigroup and the multiplicative monoid of triangular matrices over a finite field.
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